This is a multi-investigator project that applies mathematical and statistical methods to the etiology of cancer and to the elucidation of biological mechanisms relevant to cancer biology. (1) Data on experimental cancers and on the incidences of various human cancers are being compared with mathematical models that allow for growth of stem cells and the occurrence of two or more critical cancer mutations. (2) Selected international populations are being investigated for the development of hepatic cancer following infection with hepatitis B virus. Immune responses are monitored and the roles of congenital viral infection, nutritional status, and serum iron and ferritin levels evaluated. (3) Linear discriminant analysis is applied to data on the age-specific incidences of cancers of various kinds in rats as a function of early nutritional history with the objective of discovering diets conducive to reduction in risk of neoplasia. (4) The interactions of carcinogens with nucleic acids of enzymes with substrates and metals, and of proteins with drugs are being studied by X-ray crystallography and NMR spectroscopy. Theoretical molecular models are built and 3-dimensional representations displayed graphically. (5) Mathematical programs are being developed to permit the calculation of the number of molecules of a particular RNA species at a given time following viral infection and to facilitate the analysis of viral nucleotide sequence information. (6) Stochastic models are being developed for the study of antibody diversity, the analysis of family clusters, the mechanism of bacteriophage attachment, and the analysis of RNA processing during development. (7) The thermodynamic theory of fluctuations is being applied to epigenetic variation in cell biology. (8) The growth of cells in culture is being simulated by computer in order to interpret data on cell cycles. (9) New methods are being developed for the analysis of clinical research data.